Title: A collocation method for solving integral equations

Authors: A.G. Ramm

Addresses: Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA

Abstract: A collocation method is formulated and justified for numerical solution of the Fredholm second-kind integral equations. As an application the Lippmann-Schwinger equation is considered. The results obtained provide an error estimate and a justification of the limiting procedure used in the earlier papers by the author, dealing with many-body scattering problems in the case of small scatterers, and with creating materials with a desired refraction coefficient: Ramm, A.G. |Many-body wave scattering by small bodies and applications|, J. Math. Phys., Vol. 48, No. 10, 103-511; Ramm, A.G. (2008) |Wave scattering by many small particles embedded in a medium|, Phys. Lett. A, Vol. 372, No. 17, (2008), pp.3064-3070

Keywords: collocation method; integral equations; many-body scattering; refraction coefficient; small particles.

DOI: 10.1504/IJCSM.2009.027874

International Journal of Computing Science and Mathematics, 2009 Vol.2 No.3, pp.222 - 228

Published online: 13 Aug 2009 *

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